London (CNN) -- Police in London said Thursday they have arrested two men as part of an international investigation into computer hacking groups Anonymous and LulzSec.

The men, ages 24 and 20, were arrested in South Yorkshire and Wiltshire, police said. They are suspected of conspiring to commit offenses under the Computer Misuse Act of 1990.

"The arrests relate to our enquiries into a series of serious computer intrusions and online denial-of-service attacks recently suffered by a number of multinational companies, public institutions and government and law enforcement agencies in Great Britain and the United States," said Det. Mark Raymond of the Metropolitan Police Service's Central e-Crime Unit.

The name "Kayla" was used in the suspected intrusions, police said in a statement.

"Denial of service" attacks overload website servers.

Hacking groups such as Anonymous and LulzSec have claimed a number of high-profile attacks in recent months, stealing information from the U.S. Senate and Arizona state police websites, as well as data from major corporations like Sony, Bank of America and Nintendo.

They've also successfully blocked access to the websites of Visa, MasterCard, the CIA and several News Corp. newspaper websites.

Police in Britain, the United States and elsewhere have made a number of arrests of suspected "hacktivists" in recent months.